We study categories for reversible computing, focussing on reversible forms of event structures.
Event structures are a well-established model of true concurrency. There exist a number of forms
of event structures, including prime event structures, asymmetric event structures, and general event
structures. More recently, reversible forms of these types of event structures have been defined.
We formulate corresponding categories and functors between them. We show that products and co-
products exist in many cases. In most work on reversible computing, including reversible process
calculi, a cause-respecting condition is posited, meaning that the cause of an event may not be re-
versed before the event itself. Since reversible event structures are not assumed to be cause-respecting
in general, we also define cause-respecting subcategories of these event structures. Our longer-term
aim is to formulate event structure semantics for reversible process calculi.